Summary
Goal: Construct simultaneous 95% confidence intervals
1. Without contamination
Method 1:
- The coverage ratios are similar to each individual pair difference. And they are way over 95%.
- The joint coverage ratio is also much higher than the target 95%.
- Too conservative. Increasing sample size is making it even more conservative.
Method 2:
- The coverage ratios are not constant over all pair differences. One of the three pair difference would have distinct lower coverage ratio than others.
- That relatively low coverage pair difference caps the joint coverage ratio, leading to the desired 95%.
- Relatively exact. Increasing sample may lower the ratio to target.
2. With contamination
Individual Coverage:
Both methods show similiar patterns:
The more pair difference diverage to its original value, the more it tends to be affected by the mix ratio.
- true value 0.02: almost same before and after contamination -> limited impact
- true value 0.36: decreasing to 0.01 (completely replaced) -> most serious impact
Joint Coverage
Overall, method 2 has better performance than method 1.